Question:
If \({\log _2}\left( {5 + {{\log }_3}a} \right) = 3\) and \({\log _5}\left( {4a + 12 + {{\log }_2}b} \right) = 3\), then a + b is equal to
- 67
- 40
- 32
- 59
Correct Answer: 4
$5+\log _{3} a=2^{3}=8 \Rightarrow a=27$
Similarly, $4 a+12+\log _{2} b=5^{3}=125$
since $a=27,4(27)+12+\log _{2} b=125 \Rightarrow b=32$
a + b = 59.
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